%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:30:02 PM UTC 2026
% Result : Unsatisfiable 3.97s 1.30s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',associativity2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_substitution1) ).
tcf(c_58,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,plain,
equalish(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_67,plain,
product(identity,a,a),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(identity,X0,X1)
| ~ product(identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_179,plain,
( equalish(a,a)
| ~ product(identity,a,a) ),
inference(instantiation,[status(thm)],[c_178]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X4,X2,X3)
| ~ product(X0,X1,X4)
| ~ product(X1,X2,multiply(X1,X2))
| ~ product(X0,multiply(X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X0,X2)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_244,c_61]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(identity,X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_244,c_64]) ).
tcf(c_390,plain,
product(identity,multiply(b,c),multiply(b,c)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_412,plain,
~ product(a,c,multiply(b,c)),
inference(superposition,[status(thm)],[c_197,c_66]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X2)
| ~ product(identity,X0,X3)
| ~ product(identity,multiply(X0,X1),X2)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_222]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_285]) ).
tcf(c_521,plain,
equalish(b,a),
inference(superposition,[status(thm)],[c_65,c_519]) ).
tcf(c_615,plain,
! [X0: $i] :
( product(identity,b,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_521,c_305]) ).
tcf(c_622,plain,
( product(identity,b,a)
| ~ equalish(a,a) ),
inference(instantiation,[status(thm)],[c_615]) ).
tcf(c_2843,plain,
! [X0: $i] :
( product(X0,c,multiply(b,c))
| ~ product(identity,b,X0)
| ~ product(b,c,multiply(b,c))
| ~ product(identity,multiply(b,c),multiply(b,c)) ),
inference(instantiation,[status(thm)],[c_469]) ).
tcf(c_2844,plain,
( product(a,c,multiply(b,c))
| ~ product(identity,b,a)
| ~ product(b,c,multiply(b,c))
| ~ product(identity,multiply(b,c),multiply(b,c)) ),
inference(instantiation,[status(thm)],[c_2843]) ).
tcf(c_5586,plain,
product(b,c,multiply(b,c)),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_5587,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5586,c_2844,c_622,c_412,c_390,c_179,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:26:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.97/1.30 % SZS status Started for theBenchmark.p
% 3.97/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.97/1.30
% 3.97/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/1.30
% 3.97/1.30 % ------ iProver source info
% 3.97/1.30
% 3.97/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.97/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/1.30 % git: non_committed_changes: false
% 3.97/1.30
% 3.97/1.30 % ------ Parsing...% successful
% 3.97/1.30
% 3.97/1.30
% 3.97/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.97/1.30
% 3.97/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.97/1.30
% 3.97/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.97/1.30 % ------ Proving...
% 3.97/1.30 % ------ Problem Properties
% 3.97/1.30
% 3.97/1.30 %
% 3.97/1.30 % clauses 9
% 3.97/1.30 % conjectures 1
% 3.97/1.30 % EPR 6
% 3.97/1.30 % Horn 9
% 3.97/1.30 % unary 5
% 3.97/1.30 % binary 0
% 3.97/1.30 % lits 19
% 3.97/1.30 % lits eq 0
% 3.97/1.30 % fd_pure 0
% 3.97/1.30 % fd_pseudo 0
% 3.97/1.30 % fd_cond 0
% 3.97/1.30 % fd_pseudo_cond 0
% 3.97/1.30 % AC symbols 0
% 3.97/1.30
% 3.97/1.30 % ------ Input Options Time Limit: Unbounded
% 3.97/1.30
% 3.97/1.30
% 3.97/1.30 % ------
% 3.97/1.30 % Current options:
% 3.97/1.30 % ------
% 3.97/1.30
% 3.97/1.30
% 3.97/1.30 %
% 3.97/1.30
% 3.97/1.30 % ------ Proving...
% 3.97/1.30 %
% 3.97/1.30
% 3.97/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.97/1.30
% 3.97/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.30
% 3.97/1.30
%------------------------------------------------------------------------------